This disclosure is related to the field of analysis of fluid production from subsurface wellbores to evaluate expected future fluid production and ultimate total fluid production therefrom. More specifically, the disclosure relates to methods for statistical analysis of time-dependent fluid production rate and cumulative produced fluid volume measurements to obtain improved estimates of future fluid production rate and ultimate cumulative production volumes.
Statistical prediction of well fluid production rates is known in the art for use in estimating wellbore reserves and wellbore economic value. Several methods known in the art are used to quantify the uncertainty in wellbore fluid production forecasts, which is useful for representing a range of reserves in accordance with United States Securities and Exchange Commission (SEC) reserves reporting rules, and estimating the chance of commercial success of oil and gas wells given the inherent uncertainty in forecasting.
Production forecasts are engineering interpretations of fluid production volumetric or mass rate data to predict the performance of hydrocarbon producing (oil and gas) wells. Data used for production forecasts may be obtained from disparate sources, but most often when a wellbore is already producing fluids (including oil and/or gas), the data used are typically solely measurements of production rates. The fluid production rate is often displayed on a Cartesian coordinate graph wherein the fluid production rate is shown on the y-axis, and the time of measurement shown on the x-axis. An example fluid production rate graph is shown in FIG. 1. Many different versions of the same basic data display also known in the art to be used, such as log-log and semi-log axis display of the same fluid production rate data (shown in FIG. 2 and FIG. 3), as well as other transforms of the fluid production rate data. These manipulations and transforms may identify different trends used to characterize the change in fluid production rate over time, and to evaluate the quality of the fit of a model to the fluid production rate measurement data. A model may be a representation of inferred physical characteristics of a particular subsurface reservoir, such as fluid pressure, fractional volumes of pore space occupied by oil, gas and water, viscosities and composition of the reservoir fluids, geometry of the reservoir, and the drive mechanism by which fluid is moved from the reservoir to the Earth's surface.
Interpretation of the fluid production rate measurement data to generate a fluid production rate and/or cumulative produced fluid volume forecast is usually performed by analysis of the interpreter in a process of “tuning” Estimates of the parameters used in the model used for forecasting may be obtained from interpretation or diagnosis of the fluid production rate measurement data, or, when the data displays no strong indications, from analogous data such as data from geodetically proximate (“offset”) wells or subsurface reservoirs having similar characteristics. For example, a wellbore having a well-defined fluid production rate measurement trend is shown in FIG. 4, while a wellbore having fluid production rate measurement data that may be characterized as “noisy” is shown in FIG. 5.
Interpretation of fluid production rate measurement data using known techniques such as curve fitting to generate fluid production rate forecasts and/or cumulative fluid production volume forecasts typically does not include a calculation of error between the forecast and the measurement data. Such forecasts are typically performed by a human interpreter and are based at least in part on informed but subjective judgment of the human interpreter. There are limitations associated with forecasting based on such human interpretation including, for example, difficulties associated with consistently reproducing interpretations among different human interpreters, non-uniqueness of interpretations among interpreters, the inability to rapidly make interpretations using computer algorithms, the inability to quantify the uncertainty inherent in any prediction of future well production, and the requirement that the interpreter be highly skilled in the art of fluid production rate measurement data interpretation so as to make subjective judgments well informed.